sqrt * 4 x sqrt * 4 = 4 because sqrt * 4 = 2, so 2 x 2 = 4 but what about sqrt*1=1 ?

Indranil

Junior Member
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Feb 22, 2018
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why sqrt of 1 is 1?
As I know sqrt * 4 x sqrt * 4 = 4 because sqrt * 4 = 2, so 2 x 2 = 4 but what's about sqrt * 1?
 

Dr.Peterson

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Nov 12, 2017
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why sqrt of 1 is 1?
As I know sqrt * 4 x sqrt * 4 = 4 because sqrt * 4 = 2, so 2 x 2 = 4 but what's about sqrt * 1?
First, "sqrt" is not a number you can multiply ("*"). It is a function, so you write sqrt(x) to mean the square root of x.

The reason sqrt(4)*sqrt(4) = 4 is that the left hand side is (sqrt(4))^2, and by definition the square root is the inverse of squaring: that is, squaring undoes the square root. In general, (sqrt(x))^2 = x.

What is the square root of 1? By definition, it is the (non-negative) number whose square is 1. Since 1^2 = 1, we conclude that sqrt(1) = 1.
 

pka

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Jan 29, 2005
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8,099
why sqrt of 1 is 1?
As I know sqrt * 4 x sqrt * 4 = 4 because sqrt * 4 = 2, so 2 x 2 = 4 but what's about sqrt * 1?
To Indranil, You have been asked to use sqrt(x) which is standard function notation? Why don't you please do so?

If
\(\displaystyle a\ge 0 \) then \(\displaystyle sqrt(a) \) is real number having the property that \(\displaystyle \left(\sqrt{a}\right)^2=a \)
So
\(\displaystyle sqrt(1)\cdot sqrt(1)=\left(\sqrt{1}\right)^2=1 \)
 

HallsofIvy

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Jan 27, 2012
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If you are really asking "Why isn't it \(\displaystyle \sqrt{1}= \pm 1\)" its because \(\displaystyle \sqrt{x}\) is a function and functions must return one value for every x. \(\displaystyle \sqrt{x}\) is defined as "the positive number, a, such that \(\displaystyle a^2= x\)".
 
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